Question: What do the following two equations represent? $-4x-3y = -3$ $12x+9y = 5$
Explanation: Putting the first equation in $y = mx + b$ form gives: $-4x-3y = -3$ $-3y = 4x-3$ $y = -\dfrac{4}{3}x + 1$ Putting the second equation in $y = mx + b$ form gives: $12x+9y = 5$ $9y = -12x+5$ $y = -\dfrac{4}{3}x + \dfrac{5}{9}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.